Transitional vortices in wide-gap spherical annulus flow.
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity uH computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that,...
We study pressure-driven, two-layer flow in inclined channels with high density and viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics. Two distinguished limits are considered: where the viscosity ratio is small with density ratios of order unity, and where both density and viscosity ratios are small. The evolution equations account for the presence of...
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...
The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based...
The reliable and effective assimilation of measurements and numerical simulations in engineering applications involving computational fluid dynamics is an emerging problem as soon as new devices provide more data. In this paper we are mainly driven by hemodynamics applications, a field where the progressive increment of measures and numerical tools makes this problem particularly up-to-date. We adopt a Bayesian approach to the inclusion of noisy data in the incompressible steady Navier-Stokes equations...
On prouve l’unicité des solutions du système de Navier-Stokes incompressible dans , où est un domaine lipschitzien borné de ().
The main result of this paper is the proof of uniqueness for mild solutions of the Navier-Stokes equations in L3(R3). This result is extended as well to some Morrey-Campanato spaces.